Elementary Algebra

Published by Cengage Learning
ISBN 10: 1285194055
ISBN 13: 978-1-28519-405-9

Chapter 11 - Additional Topics - Chapter 11 Review Problem Set - Page 520: 72


The domain of this function is $\text{all real numbers where}\; x≠6$.

Work Step by Step

When this question asks for the domain of the function, it is asking for what values of x can be legally substituted into the function. (For instance, in the function $\frac{3}{x}$, $x≠0$ because this would make the denominator of the fraction equal to 0, making the function at that value be undefined.) In the case of the function $y=\frac{1}{x-6}$, we can't substitute $6$ into the function as it would cause the denominator to be $6-6=0$, making the fraction undefined. Therefore, the domain of this function is $\text{all real numbers where}\; x≠6$.
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